-2.1.9 Find general solution of 2y'+y=3t

  • #1
karush
Gold Member
MHB
3,269
5

2000
Find the general solution of the given differential equation, and use it to determine how
solutions behave as .


divide by 2

find integrating factor,

multiply thru
ok something went :confused::confused::confused::confused::confused:
------------------------------------
book answer
 
Last edited:
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  • #2
When you determine your integrating factor, you need only determine up to but not including the constant of integration:



And so the ODE becomes:



Or:



Integrating, we obtain:



Now does the answer given by the book make sense? :)

Hence:

 
  • #3
for some reason I thought stayed the same whether taking the integral or derivative



multiply thru

integrate through

simplify

=========================================


Draw a direction field for the given differential equation.
how do you do this with Desmos
 
Last edited:
  • #5
karush said:

simplify
Think about these two lines for a moment...

-Dan
 
  • #6
topsquark said:
Think about these two lines for a moment...

-Dan

 
Last edited:
  • #7
karush said:
You just aren't doing well with the typos today, huh? (Sun)

Whatever. You got it.

-Dan
 
  • #8
I just wanted to see if you would catch it...
😎
 

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